An asymptotic formula for the primitive of Hardy's function

作者：Jutila Matti^*

来源：Arkiv for Matematik, 2011, 49(1): 97-107.

DOI：10.1007/s11512-010-0122-4

Let Z(t) be the classical Hardy function in the theory of Riemann's zeta-function. An asymptotic formula with an error term O(T (1/6)log T) is given for the integral of Z(t) over the interval [0,T], with special attention paid to the critical cases when the fractional part of root T/2 pi is close to 1/4 or 3/4

• 出版日期2011-4